Question: Brandon is an amateur marksman. When he takes aim at a particular target on the shooting range, there is a $0.1$ probability that he will hit it. One day, Brandon decides to attempt to hit $10$ such targets in a row. Assuming that Brandon is equally likely to hit each of the $10$ targets, what is the probability that he will hit at least one of them? Round your answer to the nearest hundredth. $P(\text{at least one hit})=$
Solution: Strategy In this situation it is much easier to calculate the probability of the event we are looking for (he hits at least one target) by calculating the probability of its complement (he misses every target), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one hit})=1-P(\text{miss all }10)$ Calculations $\begin{aligned} P(\text{at least one hit})&=1-P(\text{miss all }10) \\ \\ &=1-(0.9)^{10} \\ \\ &\approx 1-0.349 \\ \\ &\approx 0.651\end{aligned}$ Answer $P(\text{at least one hit}) \approx 0.65$